Analytical models of short-range order in FCC and BCC alloys

A statistical-mechanics analysis is used to create analytic estimates for the short-range order (SRO) parameters in FCC and BCC solid solution alloys as a function of composition and temperature. As in the classic quasi-chemical method, the analysis assumes pair interactions among atoms at different distances and partitions the entire crystal into a set of identical independent clusters that are then treated like molecules in a gas. This enables analytic development of the probabilities that govern SRO. For binary and ternary alloys, increasingly complex clusters are considered that systematically extend the range of accuracy of the analytic model relative to reference Monte Carlo simulations. The results enable fast assessment of likely SRO using estimated inputs for atom-atom interaction energies. In this record we provide our analytical solution as well as the simulation data supporting our theoretical prediction of the short-range order parameter in both FCC and BCC alloys.

本研究采用统计力学分析方法，针对面心立方（Face-Centered Cubic, FCC）与体心立方（Body-Centered Cubic, BCC）固溶体合金的短程有序（short-range order, SRO）参数，构建了基于成分与温度的解析估算模型。与经典准化学方法一致，该分析假设原子间存在不同距离的成对相互作用，并将完整晶体划分为一组完全相同且相互独立的团簇，随后将这些团簇类比为气体中的分子进行处理，由此可推导得到支配短程有序行为的概率解析表达式。针对二元与三元合金，本研究考虑了复杂度逐步提升的团簇，相较于基准蒙特卡洛（Monte Carlo）模拟，该解析模型的精度覆盖范围得到系统性拓展。通过输入原子间相互作用能的估算值，该结果可实现短程有序参数的快速评估。本数据集包含我们得到的解析解，以及用于验证FCC与BCC合金短程有序参数理论预测的模拟数据。